Generally, the domain is implied to be the set of all real numbers that yield a real number functional value (in the range).
Some restrictions to domain:
1. Denominator cannot equal zero (0).
2. Radicand must be greater than or equal to zero (0).
3. Practical problems may limit domain.
In addition to working problems, you should know and understand the definitions of these words and phrases:
A set of points in a coordinate plane is the graph of
y as a function of x
if and only if no vertical line intersects the graph at more than one point.
On the interval containing x1 < x2,
1. f(x) is increasing if f(x1) < f(x2). Graph of f(x) goes up to the right.
2. f(x) is decreasing if f(x1) > f(x2). Graph of f(x) goes down to the right.
On any interval,
3. f(x) is constant if f(x1) = f(x2). Graph of f(x) is horizontal.
Increasing, Decreasing, and Constant Function
1. A function given by y = f(x) is even if, for each x in the domain, f(-x) = f(x).
2. A function given by y = f(x) is odd if, for each x in the domain, f(-x) = - f(x).